The fate of a gravitational wave in de Sitter spacetime

TL;DR

This paper investigates how a positive cosmological constant affects the propagation and detectability of gravitational waves in de Sitter spacetime, showing that detection is impeded beyond a certain critical distance related to the cosmological constant.

Contribution

It demonstrates that a positive cosmological constant limits gravitational wave detection at large distances, providing a quantitative critical length scale for this effect.

Findings

Detection of gravitational waves is hindered beyond a critical distance ${ m{f L}}_{crit}$ due to $ ext{Lambda}$.

${ m{f L}}_{crit}$ depends on wave frequency, strain, and cosmological constant.

The result implies gravitational wave signals are only interpretable if their properties are below a certain threshold set by $ ext{Lambda}$.

Abstract

If we want to explain the recently discovered accelerated stage of the universe, one of the option we have is to modify the Einstein tensor. The simplest such modification, in agreement with all observations, is the positive cosmological constant $\Lambda$. Such a modification will also have its impact on local observables and on the propagation of weak gravitational waves. We show here that the inclusion of a cosmological constant impedes the detection of a gravitational wave if the latter is produced at a distance larger than ${\cal L}_{\rm crit}=(6\sqrt{2}\pi f \hat{h}/\sqrt{5})r_{\Lambda}^2$ where $r_{\Lambda}=1/\sqrt{\Lambda}$ and $f$ and $\hat{h}$ are the frequency and the strain of the wave, respectively. ${\cal L}_{\rm crit}$ is of astrophysical order of magnitude. We interpret the result in the sense that the gravitational wave interpretation is only possible if the characteristic wave properties are smaller than the non-oscillatory solution due to $\Lambda$.